Reischel, a graduate transfer from Rhode Island who missed the Colonels last game with a sore back, made all 10 of his free throws to break the school record with 32 straight.
JaVontae Hawkins added 15 points for Eastern Kentucky (9-6), which led 45-21 at the half on the strength of 59 percent shooting (19 of 32).
Zane Waterman had 23 points for the Jaspers (3-8), who shot 24 percent in the first half (6 of 25).
EKU scored the first 16 points of the game with Reischel getting 12 with two 3-pointers and Hawkins the other two baskets. The Jaspers got it back to eight but Jaylen Babb-Harrison hit back-to-back 3-pointers to make it 26-12 and the lead was double figures the rest of the way.